There was a time when the federal government tested nuclear thermal rocket technology for the flights that would follow the Apollo moonshots. Back in the 1960s, Los Alamos National Laboratory in New Mexico and its industrial partners set up Project NERVA, which stands for Nuclear Energy for Rocket Vehicle Application. The idea was to use a nuclear reactor to heat up liquid hydrogen propellant and blast a rocket out of Earth orbit. A trip to the moon would take just 24 hours. Going to Mars? You could make the voyage in just four months.

The initial plan called for NERVA technology to power the first manned mission to Mars in 1981. More than 20 rocket tests — conducted under names such as KIWI and Phoenix, Peewee-1 and Nuclear Furnace-1 — were carried out at a Nevada test range. But qualms about nuclear power, and about the multibillion-dollar development cost, led to Project NERVA's cancellation in 1973. Instead, the Nixon administration went with the space shuttle program.

Nuclear rocket propulsion briefly returned to the spotlight in 2003, when NASA considered developing a reactor-based system for deep-space missions such as the Jupiter Icy Moon Orbiter, as part of what became known as Project Prometheus. The initial missions would have used a small reactor to generate electricity for an ion drive, rather than implementing the NERVA concept. But like NERVA, Prometheus came to be perceived as too complex and risky. NASA canceled the program in 2005.

Pat Rawlings / Bill Gleason / NASA

One concept called for a detachable module to be sent into space, then placed on a nuclear thermal rocket for a 24-hour trip to the moon.

"Harness the full intellectual and industrial strength of our universities, national laboratories and private enterprise to rapidly develop and deploy a nuclear thermal rocket (NTR) adaptable to both manned and un-manned space missions. A NTR (which would only operate in outer space) will jump-start our manned space exploration program by reducing inner solar system flight times from months to weeks. This is not new technology; NTRs were tested in the 1960s (President Kennedy was a guest at one test). The physics and engineering are sound. In addition to inspiring young Americans to careers in science, technology, engineering and mathematics, a working NTR will herald a speedy and economical expansion of the human presence in the cosmos."

The petition needs 25,000 online supporters by Feb. 2 to trigger a White House response. So far it has ... three, including VanAlstine.

"I don't have anything to do with the aerospace industry," VanAlstine told NBC News over the weekend. "I'm just into space."

"A lot of the scientists say the only way to get enough mass up and get the travel time down is to go with NTR," VanAlstine said. "I'm not an engineer or anything, but that's what all the smart guys are saying. ... It's never going to be like '2001' without going with the nuclear thermal rocket."

NASA already has a big rocket project on its hands: the effort to develop a new Orion exploration spaceship and a conventional heavy-lift rocket capable of sending humans beyond Earth orbit by the early 2020s, at a cost that could amount to $35 billion. It may turn out that taking on nuclear thermal propulsion right now is as unrealistic as building a Death Star or the Starship Enterprise. But VanAlstine is soldiering on — and dreaming of the day when spaceflight will be as quick and easy as it looked in "2001: A Space Odyssey."

"It's not me that's going to go into space," said VanAlstine, who turns 49 on Wednesday. "But maybe my nephew will be riding this."

What do you think? Feel free to weigh in on the prospects for space nuclear power in a comment below.

Update for 9 p.m. ET Jan. 9: It turns out that NASA is still studying the nuclear thermal rocket concept, using non-nuclear materials. Today, the space agency provided an update on the Nuclear Cryogenic Propulsion Stage project. The project's researchers are using Marshall Space Flight Center's Nuclear Thermal Rocket Element Environmental Simulator, or NTREES, to test various composite materials as potential fuel elements. Check out the full report.

Update for 3:30 p.m. ET April 2: The White House petition didn't receive the required 25,000 online signatures by the Feb. 2 deadline. "However, we didn't do too bad: 2,937 signed it," the campaign said on its Facebook page.